1. Field of the Invention
The invention relates to a phase tracking device, and more particularly to a method for synchronizing the carrier frequency and sampling clock frequency in an orthogonal frequency division multiplexing system.
2. Description of the Related Art
OFDM (Orthogonal Frequency Division Multiplexing) is a widely used data transmission technique, which divides a wideband channel into multiple narrowband sub-channels to carry out simultaneous transmission of the sub-carriers. Although the sub-carriers are overlapped in the frequency spectrum, they do not interfere with each other due to their orthogonality.
OFDM is sensitive to synchronization errors due to the narrow sub-carrier spacing. Synchronization errors comprise CFO (carrier frequency offset) and SFO (sampling frequency offset). CFO is caused by the mismatch of the oscillation frequency between the transmitter and receiver, Doppler effect, and phase noise, while SFO is caused by the mismatch of the sampling clock cycle between the transmitter and receiver.
The algorithm for tracking CFO and SFO must evaluate the drift phase of each pilot for each OFDM symbol. However, in the time dispersive channel, the pilot may locate in the decline of the channel and thus suffers from low signal to noise ratio (SNR).
In “Joint Weighted Least-Square Estimation of Carrier-Frequency Offset and Timing Offset for OFDM Systems Over Multi-path Fading Channels” issued by Pei-Yun Tasi discloses the weighted least square (WLS) algorithm for overcoming the described problem.
FIG. 1 illustrates a conventional phase compensating circuit comprising sampler 102, phase compensator 104, FFT (Fast Fourier Transform) circuit 106, coarse synchronization circuit 108, and phase tracking circuit 110.
First, in the training stage of a packet, a CFO estimate and an estimated symbol boundary index are generated by coarse synchronization circuit 108 according to the preamble portion of the received signal. The phase of the subsequent received signal is then adjusted by phase compensator 104 according to the estimated symbol boundary and the initial CFO estimate. An estimated channel Ĥl,k is generated through exploiting the initially adjusted received signal by a channel estimator.
The receiver then enters a phase tracking stage. FFT circuit 106 transforms the initially adjusted received signal into frequency domain according to the estimated symbol boundary. A phase error ∠Xl,m of two time adjacent pilots in the same sub-carrier is generated by phase tracking circuit 1 10 with CORDIC (Coordinate Rotation Digital Computer) circuit, and a sampling frequency adjusting signal {circumflex over (δ)}l and a carrier frequency adjusting signal {circumflex over (ε)}l are produced according to the WLS algorithm. The equation of the WLS algorithm is as follow:
                    ɛ        ^            l        =                                                                                        ∑                                      m                    ∈                    M                                                  ⁢                                                      (                                                                                                                                                  H                                                          l                              ,                              m                                                                                                                                2                                            ·                                              m                        2                                                              )                                    ·                                                            ∑                                              m                        ∈                        M                                                              ⁢                                          (                                                                                                                                                                                                H                                                                  l                                  ,                                  m                                                                                                                                                    2                                                    ·                          ∠                                                ⁢                                                                                                  ⁢                                                  X                                                      l                            ,                            m                                                                                              )                                                                                  -                                                                                          ∑                                  m                  ∈                  M                                            ⁢                                                (                                                                                                                                      H                                                      l                            ,                            m                                                                                                                      2                                        ·                    m                                    )                                ·                                                      ∑                                          m                      ∈                      M                                                        ⁢                                      (                                                                                                                                                                                  H                                                              l                                ,                                m                                                                                                                                          2                                                ·                        ∠                                            ⁢                                                                                          ⁢                                              X                                                  l                          ,                          m                                                                                      )                                                                                                            (                      2            ⁢            π            ⁢                                          N                S                            N                                )                ⁡                  [                                                    ∑                                  m                  ∈                  M                                            ⁢                                                                                                              H                                              l                        ,                        m                                                                                                  2                                ·                                                      ∑                                          m                      ∈                      M                                                        ⁢                                      (                                                                                                                                                  H                                                          l                              ,                              m                                                                                                                                2                                            ·                                              m                        2                                                              )                                                                        -                                          (                                                      ∑                                          m                      ∈                      M                                                        ⁢                                      (                                                                                                                                                  H                                                          l                              ,                              m                                                                                                                                2                                            ·                      m                                        )                                                  )                            2                                ]                                        δ        ^            l        =                                                                                        ∑                                      m                    ∈                    M                                                  ⁢                                                      (                                                                                                                    H                                                      l                            ,                            m                                                                                                                      2                                        )                                    ·                                                            ∑                                              m                        ∈                        M                                                              ⁢                                          (                                                                                                                                                                                                H                                                                  l                                  ,                                  m                                                                                                                                                    2                                                    ·                          ∠                                                ⁢                                                                                                  ⁢                                                                              X                                                          l                              ,                              m                                                                                ·                          m                                                                    )                                                                                  -                                                                                          ∑                                  m                  ∈                  M                                            ⁢                                                (                                                                                                                                      H                                                      l                            ,                            m                                                                                                                      2                                        ·                    m                                    )                                ·                                                      ∑                                          m                      ∈                      M                                                        ⁢                                      (                                                                                                                                                                                  H                                                              l                                ,                                m                                                                                                                                          2                                                ·                        ∠                                            ⁢                                                                                          ⁢                                              X                                                  l                          ,                          m                                                                                      )                                                                                                            (                      2            ⁢            π            ⁢                                          N                s                            N                                )                ⁡                  [                                                    ∑                                  m                  ∈                  M                                            ⁢                                                                                                              H                                              l                        ,                        m                                                                                                  2                                ·                                                      ∑                                          m                      ∈                      M                                                        ⁢                                      (                                                                                                                                                  H                                                          l                              ,                              m                                                                                                                                2                                            ·                                              m                        2                                                              )                                                                        -                                          (                                                      ∑                                          m                      ∈                      M                                                        ⁢                                      (                                                                                                                                                  H                                                          l                              ,                              m                                                                                                                                2                                            ·                      m                                        )                                                  )                            2                                ]                    
wherein Ĥl,k is the estimated channel, ∠Xl,m is the phase error, l is the index of the OFDM symbol, m is the index of the sub-carrier, M is a set of all pilot indexes, N stands for N-point FFT, and Ns is the OFDM symbol length. Then, sampler 102 outputs newly sampled signal according to the sampling frequency adjusting signal {circumflex over (δ)}l, while phase compensator 104 adjusts the newly sampled signal according to the carrier frequency adjusting signal {circumflex over (ε)}l.
The WLS algorithm described above may cause excessive delay and power consumption due to the high complexity in the channel weighting and phase error calculation process.